Simulations of overstable inertial-acoustic modes in black hole accretion discs

Abstract

We present two-dimensional inviscid hydrodynamic simulations of overstable inertial-acoustic oscillation modes (p modes) in black hole accretion discs. These global spiral waves are trapped in the innermost region of the disc, and are driven overstable by wave absorption at the corotation resonance (rc) when the gradient of the background disc vortensity (vorticity divided by surface density) at rc is positive and the disc inner boundary is sufficiently reflective. Previous linear calculations have shown that the growth rates of these modes can be as high as 10 per cent of the rotation frequency at the disc inner edge. We confirm these linear growth rates and the primary disc oscillation frequencies in our simulations when the mode amplitude undergoes exponential growth. We show that the mode growth saturates when the radial velocity perturbation becomes comparable to the disc sound speed. During the saturation stage, the primary disc oscillation frequency differs only slightly (by less than a few per cent) from the linear mode frequency. Sharp features in the fluid velocity profiles at this stage suggest that the saturation results from non-linear wave steepening and shock dissipation. © 2013 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.